"This city is my home."
Translation:Этот город — мой дом.
1) "Города" = "cities" in the nominative and the accusative cases. 2) "This is my home." = "Это мой дом.", but when "this" is before a noun then its translation depends on a gender of the translated noun. "Город" is masculine, therefore "Этот город - мой дом."
Example: "This ring is my precious". The "ring" in Russian has a neutral gender, the "precious" as a noun in Russian has a feminine gender, therefore "Это кольцо - моя прелесть.".*
*This translation of "my precious" ("моя прелесть") is traditional in Russia for films "The Lord of the Rings" and memes.
это means 'that/this is'.
You need to use the masculine demonstrative pronoun этот.
You will want to read 'A Guide to Using ЭТО', by olimo, found here: >> https://www.duolingo.com/comment/11536858
As far as my incomplete understanding of the subject goes, it comes down to "это <noun>" meaning "the <noun>" and "этот <noun>" meaning "This particular variant of <noun>," where этот can be replaced by the particular version required for amount(singular/plural) and gender(male/female/neutral).
Do read the guide, it is far more helpful than any single comment I can give you.
There are two distintions: это моя сестра: This is my sister. "This is" is (nearly?) always это. Then you need it as a determiner: * этот стол ...: this table * эта машина ...: this car * это кресло ...: this armchair * эти карты ...: these maps
And you need to change them according to gender and case: цвет этого стола, на этой машине